To calculate the receptive field, for a given node in the network and a given input image, we compute the gradient of the activation of that node with respect to the image.
The saliency map is a grayscale image, obtained by taking the absolute value of the gradient for each pixel and summing across the three color channels [1]}.
The saliency map is normalized, such that the sum across pixels is one, and is interpreted as a 2-dimensional probability density.
The receptive field size is computed by the square root of the total variance (the trace of the covariance matrix) of that density.
We use the total variance since it quantifies the scatter of the saliency map along both axes independently.
The receptive field shape is defined as the ellipsoid containing 3 standard deviations on both axes.
